The approach to process semantics using quantales and modules is topologized by considering tropological systems whose sets of states are replaced by locales and which satisfy a suitable stability axiom. A corresponding notion of localic sup-lattice (algebra for the lower powerlocale monad) is described, and it is shown that there are contravariant functors… (More)

We study properties of the quantale spectrum Max A of an arbitrary unital C*-algebra A. In particular we show that the spatializa-tion of Max A with respect to one of the notions of spatiality in the literature yields the locale of closed ideals of A when A is commuta-tive. We study under general conditions functors with this property, in addition requiring… (More)

We present a dynamic form of observational logic for specifying concurrent systems on the basis of their observable behaviour, in particular without needing a language for describing states, which are regarded as non-observable. The logic is based on quantales. The models are labelled transition systems, and a weakly complete proof system is presented. We… (More)

The Kripke semantics of classical propositional normal modal logic is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. This algebraic semantics subsumes the traditional algebraic semantics based on lattices with unary operators, and it suggests natural interpretations of modal logic, of… (More)

We revisit sheaves on locales by placing them in the context of the theory of Hilbert quantale modules. The local homeomorphisms p : X → B are identified with the locales X that are Hilbert B-modules equipped with a natural notion of basis. These modules form a full subcategory B-HMB of the category of Hilbert B-modules where all the homomorphisms are… (More)

We propose a process algebra, the Algebra of Behavioural Types. A type is a higher-order labelled transition system that characterises all possible life cycles of a concurrent object. States represent interfaces of objects; state transitions model the dynamic change of object interfaces. Moreover, a type provides an internal view of the objects that inhabit… (More)